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a) \(3x^2-3y^2=3\left(x^2-y^2\right)=3\left(x-y\right)\left(x+y\right)\)
b) \(x^2-xy+7x-7y=\left(x^2+7x\right)-\left(xy+7y\right)\)
\(=x\left(x+7\right)-x\left(y+7\right)=x\left(x+7-y-7\right)=x\left(x-y\right)\)
c)\(x^2-3x+2=x^2-2x-x+2=\left(x^2-x\right)-\left(2x-2\right)\)
\(=x\left(x-1\right)-2\left(x-1\right)=\left(x-2\right)\left(x-1\right)\)
d) \(x^3+2x^2y+xy^2-16x=x\left(x^2+2xy+y^2-16\right)\)
\(=x\left[\left(x+y\right)^2-16\right]=x\left(x+y-4\right)\left(x+y+4\right)\)
\(4x^4-9x^2\)
\(=\left(2x^2\right)^2-\left(3x\right)^2\)
\(=\left(2x^2-3x\right)\left(2x^2+3x\right)\)
c) \(\left(x^2-x+6\right)^2+\left(x-3\right)^2\)
\(=-\left(\left(x^2+x-6\right)-\left(x+3\right)^2\right)\)
\(=-\left(x^2+x-6-x-3\right)\left(x^2+x+6+x+3\right)\)
\(=-\left(x^2-9\right)\left(x^2+2x+9\right)\)
\(=-\left(\left(x-9\right)\left(x+9\right)\left(x^2+2x+9\right)\right)\)
a) 7x2 - 14xy + 7y2
= 7(x2 - 2xy + y2)
= 7(x - y)2
b) x2 + 3x - 10
= - ( x2 - 3x + 10 )
= - ( x2 - 2 . 3/2x + 9/4 + 31/4 )
= - (( x - 3/2 )2 + 31/4
= (x - 3/2)2 - \(\left(\sqrt{\frac{31}{4}}\right)^2\)
= \(\left(x-\frac{3}{2}-\sqrt{\frac{31}{4}}\right)\left(x-\frac{3}{2}+\sqrt{\frac{31}{4}}\right)\)
1) 3x2y+6xy+3y= 3y.(x2+2x+1) = 3y.(x+1)2
2) 12x-4x2-9+a2 = a2-(4x2-12x+9)= a2-(2x-3)2= (a+2x-3).(a-2x+3)
3) x3-7x-6 = x3-2x2+2x2-4x-3x+6 = x2.(x-2)+2x.(x-2)-3.(x-2)= (x-2).(x2+2x-3) = (x-2).(x2+x-3x-3)= (x-2).(x+1).(x-3)
a) \(5a\left(x-3y\right)+8\left(3y-x\right)\)
\(=5a\left(x-3y\right)-8\left(x-3y\right)\)
\(=\left(x-3y\right)\left(5a-8\right)\)
b) \(7x^2-14xy+7y^2-7z^2\)
\(=7\left(x^2-2xy+y^2-z^2\right)\)
\(=7\left[\left(x^2-2xy+y^2\right)-z^2\right]\)
\(=7\left[\left(x-y\right)^2-z^2\right]\)
\(=7\left(x-y-z\right)\left(x-y+z\right)\)
a) 5a(x-3y) + 8(3y-x)
= 5a(x-3y) - 8(x-3y)
=(5a-8)(x-3y)